Directed n-Superhypergraphs Incorporating Bipolar Fuzzy Information: A Multi-Tier Framework for Modeling Bipolar Uncertainty in Complex Networks
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Graph theory studies the mathematical structures of vertices and edges to model relationships and connectivity. Hypergraphs extend this framework by allowing hyperedges to connect arbitrarily many vertices at once [1], and Super-HyperGraphs further generalize hypergraphs via iterated powerset constructions to capture hierarchical linkages among edges [2, 3]. Bipolar fuzzy directed graphs assign positive and negative membership degrees to directed edges and vertices, and bipolar fuzzy directed hypergraphs extend this assignment to multi-vertex hyperedges. In this paper, we extend directed Super-HyperGraphs by incorporating bipolar fuzzy membership and introduce the Bipolar Fuzzy Directed n-Super-HyperGraph, whose structural properties we investigate.